x^2=16-8x

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Solution for x^2=16-8x equation:


Simplifying
x2 = 16 + -8x

Solving
x2 = 16 + -8x

Solving for variable 'x'.

Reorder the terms:
-16 + 8x + x2 = 16 + -8x + -16 + 8x

Reorder the terms:
-16 + 8x + x2 = 16 + -16 + -8x + 8x

Combine like terms: 16 + -16 = 0
-16 + 8x + x2 = 0 + -8x + 8x
-16 + 8x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-16 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 8x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 8x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 8x + x2 = 0 + 16
8x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
8x + x2 = 16

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 16 + 16

Reorder the terms:
16 + 8x + x2 = 16 + 16

Combine like terms: 16 + 16 = 32
16 + 8x + x2 = 32

Factor a perfect square on the left side:
(x + 4)(x + 4) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + 4) equal to 5.656854249 and -5.656854249.

Subproblem 1

x + 4 = 5.656854249 Simplifying x + 4 = 5.656854249 Reorder the terms: 4 + x = 5.656854249 Solving 4 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.656854249 + -4 x = 5.656854249 + -4 Combine like terms: 5.656854249 + -4 = 1.656854249 x = 1.656854249 Simplifying x = 1.656854249

Subproblem 2

x + 4 = -5.656854249 Simplifying x + 4 = -5.656854249 Reorder the terms: 4 + x = -5.656854249 Solving 4 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.656854249 + -4 x = -5.656854249 + -4 Combine like terms: -5.656854249 + -4 = -9.656854249 x = -9.656854249 Simplifying x = -9.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.656854249, -9.656854249}

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